# Jacobi elliptic function sn,cn,dn (chart) Calculator

## Calculates a table of the Jacobi elliptic function sn(u,k), cn(u,k) and dn(u,k) and draws the chart.

 k -1≦k≦1 [ initial value u increment repetition ]
 $\normal Jacobi\ elliptic\ functions\\\hspace{120} sn(u,k),\ cn(u,k),\ dn(u,k)\\[10](1)\ sn(u,k)=sin(am(u,k))\\[10](2)\ am(u,k)=\phi=F^{-1}(u,k)\\\hspace{25}u=F(\phi,k)={\large\int_{\small 0}^{\hspace{25pt}\phi}\frac{d\theta}{\sqrt{1-k^2sin^2\theta}}}\\[10](3)\ cn(u,k)=\sqrt{1-sn^2(u,k)}\\\hspace{25}dn(u,k)=\sqrt{1-k^2sn^2(u,k)}\\[10](4)\ sn^2(u,k)+cn^2(u,k)=1\\\hspace{25}k^2sn^2(u,k)+dn^2(u,k)=1\\$

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